Stability analysis of complex-valued impulsive systems with time delay

Xu, Zheng; Li, Chuandong; Huang, Tingwen; He, Xing

doi:10.1016/j.amc.2015.01.006

Cited by 16 publications

(4 citation statements)

References 31 publications

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“…To data, impulsive perturbation problem has been widely investigated [89,91,13,113,92,40,65,58,38,43,73,67,102,90,69,70,120]. For example, in [113], the global exponential stability of complex-valued impulsive systems was addressed. Some new sufficient conditions were obtained to guarantee the global exponential stability by the Lyapunov-Razumikhin theory.…”

Section: Impulsive Delayed Systemsmentioning

confidence: 99%

Review of stability and stabilization for impulsive delayed systems

Xiao

Li²,

Xi³

et al. 2018

Mathematical Biosciences &Amp; Engineering

167

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This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.

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Section: Impulsive Delayed Systemsmentioning

confidence: 99%

Review of stability and stabilization for impulsive delayed systems

Xiao

Li²,

Xi³

et al. 2018

Mathematical Biosciences &Amp; Engineering

167

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show abstract

“…For example, two-layer real-valued neural networks cannot solve the problems of exclusive "OR" (XOR) and symmetry detection, while two-layer complex-valued neural networks can easily do so, which shows that the computational ability of complex-valued neurons is remarkable. In recent years, practical applications of complex-valued neural networks in physical systems such as electromagnetic, optical, ultrasonic, and quantum waves, as well as in the fields of filtering, speech synthesis, and remote sensing, have attracted widespread attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

Zhang

Yang

2021

Physics

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The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.

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“…Stability criteria for timedelayed systems are created also via LMI [18,19]. Complexvalued neural networks with time delays are attached in [20][21][22]. As a matter of fact, when time delay occurs in dynamics and/or their derivatives, the characteristic polynomials are quasi-polynomials in one variable and its exponential powers [4,23] that are of infinite degree.…”

Section: Introductionmentioning

confidence: 99%

Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems

Zhou

Gao

2018

Mathematical Problems in Engineering

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Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

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Stability analysis of complex-valued impulsive systems with time delay

Cited by 16 publications

References 31 publications

Review of stability and stabilization for impulsive delayed systems

Review of stability and stabilization for impulsive delayed systems

Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems

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